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MELTS_Excel: A Microsoft Excel-based MELTS interface for research and
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teaching of magma properties and evolution
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Guilherme A. R. Gualda, Earth & Environmental Sciences, Vanderbilt University, Nashville,
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Tennessee, USA.
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Mark S. Ghiorso, OFM Research - West, Seattle, Washington, USA.
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Corresponding author: G. A. R. Gualda, Earth & Environmental Sciences, Vanderbilt University,
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Nashville, TN 37235, USA. ([email protected])
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Key points
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Rhyolite-MELTS interface based on Microsoft Excel
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Abstract
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The thermodynamic modeling software MELTS is a powerful tool for investigating crystallization
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and melting in natural magmatic systems. Rhyolite-MELTS is a recalibration of MELTS that
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better captures the evolution of silicic magmas in the upper crust. The current interface of
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rhyolite-MELTS, while flexible, can be somewhat cumbersome for the novice. We present a new
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interface that uses web services consumed by a VBA backend in Microsoft Excel©. The interface
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is contained within a macro-enabled workbook, where the user can insert the model input
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information and initiate computations that are executed on a central server at OFM Research.
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Results of simple calculations are shown immediately within the interface itself. It is also
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possible to combine a sequence of calculations into an evolutionary path; the user can input
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starting and ending temperatures and pressures, temperature and pressure steps, and the
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prevailing oxidation conditions. The program shows partial updates at every step of the
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computations; at the conclusion of the calculations, a series of data sheets and diagrams are
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created in a separate workbook, which can be saved independently of the interface.
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Additionally, the user can specify a grid of temperatures and pressures and calculate a phase
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diagram showing the conditions at which different phases are present. The interface can be
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used to apply the rhyolite-MELTS geobarometer. We demonstrate applications of the interface
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using an example early-erupted Bishop Tuff composition. The interface is simple to use and
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flexible, but it requires an internet connection. The interface is distributed for free from
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melts.ofm-research.org.
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Index terms
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1011, 3611, 8411, 1009, 3610, 8410, 3618, 3619, 1065
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Keywords
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Rhyolite-MELTS, thermodynamics, phase equilibria, software
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1. Introduction
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The thermodynamic modeling software MELTS [Ghiorso and Sack, 1995; Asimow and Ghiorso,
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1998] and its derivatives [e.g. pMELTS, Ghiorso et al., 2002] comprise a powerful and much
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utilized set of tools for investigating crystallization and melting in natural magmatic systems
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[e.g. Ghiorso, 1997; Ghiorso and Gualda, 2015]. Rhyolite-MELTS [Gualda et al., 2012a] is a
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recent recalibration of MELTS aimed at better capturing the evolution of silicic magmas present
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in upper crustal systems (up to ~400 MPa pressure), while maintaining the fidelity of the
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original calibration to mafic and alkalic systems. Rhyolite-MELTS also includes many algorithmic
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modifications that improve computational performance when compared to MELTS [Ghiorso,
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2013].
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Currently, most users of MELTS, pMELTS, and rhyolite-MELTS rely on a graphical user interface
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(GUI) that runs on UNIX/LINUX-based systems, primarily Intel-based Mac OS X computers. One
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of the difficulties with deployment of the GUI is that it has to be built for each of the several
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existing computer architectures and operating systems. Also, while the GUI provides a powerful
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and flexible interface, the many options available in the GUI lead to a relatively steep learning
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curve for the novice user. Finally, there is currently no graphical output of the simulation
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results, and the output from the GUI is in the form of text files that need to be processed
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offline. For all these reasons, while MELTS and its derivatives are widely used for research
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purposes, there is substantial interest in the community for a version of MELTS for other
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operating systems and computer architectures. Further, these characteristics are probably the
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main reason why MELTS – despite great potential – has not been used more frequently for
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teaching purposes. The program PhasePlot (http://www.phaseplot.org/) is a modern graphic
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interface that allows quick visualization of computations performed using rhyolite-MELTS and
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pMELTS [see Ghiorso and Gualda, 2015], which makes it an ideal tool for some teaching
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purposes. However, PhasePlot is not designed for output of quantitative data, and there are
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some limitations to the types of calculations possible, which limits its use for many types of
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applications.
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In this paper we present a new interface for rhyolite-MELTS developed in Microsoft Excel©. We
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aim to create a more interactive tool, which is easy to use, available to a widespread audience,
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and useful for both research and teaching. We first introduce the new interface, and we then
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present some examples of applications that can be developed with this interface. Finally, we list
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some of the current limitations of the new interface.
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2. The new interface
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MELTS_Excel uses web services consumed by a VBA backend client; all calculations are
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performed on the servers at OFM Research and Excel is used as an interface to send, receive,
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and process data exchanged with the server. One key advantage of this approach is that, with
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calculations being performed on servers, the only requirement for the end-user machine is for it
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to be able to run a version of Excel compatible with REST protocol web services (currently,
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Excel 2010 and 2013 for Microsoft Windows operating systems). The interface requires no
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installation, allowing use on machines regardless of the administrative privileges of the user;
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and there is no need for upgrades in the computation engine, given that all calculations are
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performed in a centrally maintained server. Further, the spreadsheet and graphic capabilities of
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Excel can be used to create formatted output, including both data and diagrams. The main
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disadvantage of the approach is that the interface requires an active internet connection to
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communicate with the OFM Research server that performs computations.
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The interface is contained within a macro-enabled workbook where composition and conditions
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are set, which includes several sheets: (1) one sheet for simple calculations and display of live
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results, where the user can insert the model input information and trigger simple calculations,
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and where a summary of results for any given condition is given; (2) one sheet listing
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properties of all phases present at any given condition; (3) one sheet where the user can select
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phases to include or exclude in the calculations; and (4) one sheet where the user can specify
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sequences of calculations (variable T, P, or both, plus fO2).
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For calculations at one given condition, the results are immediately displayed within prespecified
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fields within the interface. For instance, a user can very rapidly determine the temperature at
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which a magma of a given composition is completely molten (i.e. find the liquidus); or
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determine which phases are present, in what abundances, their compositions, and their physical
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properties (e.g. density, viscosity) at any given combination of temperature, pressure and
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oxygen fugacity.
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It is also possible to combine a sequence of calculations into an evolutionary path. The user can
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input starting and ending temperatures and pressures, temperature and pressure steps, and the
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prevailing oxidation conditions. Additionally, the user can specify a grid of temperatures and
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pressures and calculate a phase diagram in temperature-pressure space. At the conclusion of
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the calculations, a series of data sheets and diagrams are created in a separate workbook,
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which can be saved independently of the interface. This way, the user can save the results
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separately from the interface, and the interface can be used repeatedly. The results workbook
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includes several sheets, including: (a) sheets with data for each phase (equivalent to [phase
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name].tbl files from the GUI); (b) one sheet with data for the whole system (previously
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included in melts-liquid.tbl); (c) one sheet with data for total solids (previously included in
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melts-liquid.tbl); (d) one sheet including mass, volume, density evolution of each phase, solids,
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and whole system as a function of temperature, pressure, fO2; (e) charts with evolution of mass,
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volume, density as a function of temperature; (f) charts with compositional evolution of each
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phase as a function of temperature; (g) one sheet with affinities for all phases at all
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temperatures (useful for calculation of activities relative to mineral saturation); and (h) one
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sheet with initial conditions, a reference of the conditions employed in the calculation that can
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be used for easy reproduction of the simulation. The routines used to create the output can also
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be used to process tbl files returned by the GUI to create equivalent output in Excel.
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3. Some examples
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We present below a few examples that illustrate some of the capabilities of the interface. We
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start with examples that reproduce capabilities available in the GUI, and then present examples
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of applications facilitated by the new interface.
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3.1. A simple calculation
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We first present the case of a calculation performed at a single set of conditions (pressure,
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temperature, oxygen fugacity) for a given bulk composition. After entering the bulk composition
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of interest, the user has a number of options:
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(1) Equilibrate: For the bulk composition and set of conditions specified, MELTS calculates
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the phases present, their compositions and abundances, as well as the thermodynamic
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properties of each phase present;
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(2) Find liquidus: For the bulk composition, pressure and oxygen fugacity specified, MELTS
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calculates the temperature at which the only remaining phase is liquid; note that MELTS
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will try to dissolve all excess water by simply adjusting the temperature, such that
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unexpected results may occur for water-oversaturated systems;
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(3) Find wet liquidus: Similar to “Find liquidus”, except that it allows for excess water to be
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present with liquid at the calculated liquidus temperature; the results of both “Find
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liquidus” and “Find wet liquidus” will be the same if the system does not contain free
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water at the liquidus;
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(4) Compute redox: This option will partition FeO and Fe2O3 based on the specified oxygen
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fugacity value; this option is only useful when performing unconstrained redox
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calculations, in which case MELTS will use the ratio of Fe2+/Fe3+ to determine the
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oxidation state; for calculations in which fO2 is constrained, MELTS recalculates the
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Fe2+/Fe3+ using total Fe, irrespective of how FeO and Fe2O3 are partitioned in the input
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values;
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(5) Normalize: This recalculates the bulk composition so that the sum of the oxides is 100;
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this calculation is immaterial for MELTS, as it assumes that the quantities entered are
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grams of each oxide;
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(6) Normalize anhydrous: Recalculates the bulk composition so that the sum of oxides,
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except water, is 100; this is also immaterial for MELTS and only for the convenience of
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the user;
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(7) In the event that the user would like to exclude phases from the calculations, the sheet
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“Phases” should be selected, and the box next to each phase to be excluded should be
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unchecked.
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After performing computations with “Equilibrate”, “Find liquidus”, or “Find wet liquidus”, a
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summary of the resulting phase properties is displayed in the “Input” sheet, while more detailed
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results are displayed in the “Results” tab. Only phases calculated to be present are displayed in
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the “Results” sheet, while the affinities [for details, see Ghiorso and Gualda, 2013] of each
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phase included in the computation are also shown in the “Input” sheet.
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In Figure 1, we show a screenshot illustrating the results of a calculation performed using
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“Equilibrate” for a composition representative of the early-erupted Bishop Tuff [from Hildreth,
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1979], under water-saturated conditions, and fugacity constrained to the Ni-NiO buffer, at a
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temperature of 755 ºC and pressure of 175 MPa. Clicking on “Find wet liquidus” would lead to
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the temperature being reset to 760.3 ºC, with 4.34 g of water present. In this case, “Find
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liquidus” would give a physically implausible result given that a substantial amount of excess
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water is present at the liquidus. Readjusting H2O to 4.00 would cause both “Find liquidus” and
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“Find wet liquidus” to calculate a liquidus temperature of 798.9 ºC.
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We expect that using the interface in this mode will greatly facilitate building intuition about
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magmas and their properties. This mode will also be useful for selecting parameters for more
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complex calculations including sequences and grids described below.
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3.2. An isobaric sequence of calculations
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One of the most common uses of MELTS is to perform isobaric calculations that span a range of
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temperatures with a specified temperature step. One of the advantages of the new interface is
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that it is straightforward to use simple calculations like those presented above to constrain the
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temperature interval over which to perform a sequence of calculations. Using the same
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composition and pressure as the example above, we use the “wet liquidus” temperature as the
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starting point, and we find that a temperature range of only 10 ºC leads to substantial (>50 wt.
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%) crystallization [Gualda et al., 2012a; Gualda et al., 2012b]. We thus run a sequence of
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calculations by filling out the fields in the “Sequences” sheet:
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(1) T1, T2, and ΔT are the starting temperature, ending temperature, and temperature
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step, respectively; we usually use T1 as the highest temperature, with positive ΔT
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representing a decrement, because a down-temperature calculation is more efficient
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computationally; but we emphasize that, at least for equilibrium calculations, the order
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in which the calculations are performed is immaterial to the final result, given that each
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calculation represents a thermodynamic equilibrium state that is thus independent of the
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path leading to that state [Ghiorso and Gualda, 2015]; for fractionation or assimilation
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calculations, the results are intrinsically dependent upon the sequence of the
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calculations;
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(2) P1, P2, and ΔP are the pressure equivalents of the quantities above; for an isobaric
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calculation, both P1 and P2 should be set to the same values, while ΔP could have any
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value;
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(3) fO2 represents the oxygen fugacity constraints to be used in the calculation; for
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constrained calculations (“Constrained” box checked) the user can enter the oxygen
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fugacity relative to a variety of buffers, while for unconstrained calculations the FeO and
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Fe2O3 values in the “Input” sheet are used to calculate the initial oxygen fugacity
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condition, and fO2 is allowed to vary as the calculations progress [Ghiorso and Gualda,
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2015];
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(4) The user would hit the “Run PT Sequence” button to trigger the sequence of
calculations.
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Using the same composition as the example above, we perform an isothermal calculation from
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765 to 755 ºC in 0.5 ºC steps, at 175 MPa and fO2 constrained along the Ni-NiO buffer. The
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calculations take place over several seconds, with partial updates shown in the “Input” sheet as
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the calculation progresses. At the end of the calculation, Excel switches to the resulting
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workbook, which includes all the data generated during the calculations and a number of
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automatically generated diagrams (some of which are shown in Figure 2).
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While the example focuses on an isobaric calculation, the interface also allows for isothermal
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calculations under variable pressure, as well as calculations in which both temperature and
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pressure vary simultaneously. In the latter, the number of steps is chosen between the
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temperature and pressure inputs as the one that leads to the larger number of steps, and both
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temperature and pressure are varied continuously from T1 and P1 to T2 and P2. In all cases,
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the output diagrams are constructed as a function of temperature, which will render them less
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useful for isothermal calculations.
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One of new features of the Excel interface, which distinguishes it from the GUI, is that it
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includes in the output the affinities of all phases included in the calculation. The affinities can be
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useful in that they relate quite simply to the activities of the corresponding components
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[Ghiorso and Gualda, 2013], which can be helpful in the application of Ti-in-quartz, Ti-in-zircon,
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and Zr-in-titanite geobarometers [Ferry and Watson, 2007; Hayden et al., 2008; Thomas et al.,
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2010; Wark and Watson, 2006]. We demonstrate here the capabilities by calculating aTiO2 as a
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function of temperature from the calculation output. Because both T and aTiO2 are known, we
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can also compute the expected variation in Ti-in-zircon concentration as a function of
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temperature (Figure 3). Interestingly, the observed compositions of early-erupted zircon [Reid
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et al., 2011] are consistent with crystallization primarily at temperatures below 758 ºC, which
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matches the temperature interval over which crystallization of early-erupted magmas should
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have taken place (see Figure 2).
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3.3. A phase diagram calculation
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Another new feature in comparison with the GUI is that phase diagram calculations can be
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easily performed with the new interface, with a graphic output being generated automatically.
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The calculation is also called using the “Sequences” sheet. In this case, the user sets both
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temperature and pressure intervals and decrements, again with a choice of fO2 conditions. A
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grid of points in temperature-pressure space is created and a full calculation is performed for
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each grid point.
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The main concern with this type of calculation is that the number of calculations increases very
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rapidly, and individual phase diagram calculations can take from several minutes to many
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hours. Simple calculations, as well as PhasePlot, can be used to constrain the range of
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parameters to be used. Phase diagram calculations are performed as a series of isobaric
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sequences. To avoid unnecessary calculations, for each sequence (i.e. pressure), calculations
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for temperatures greater than the wet liquidus are skipped; similarly, calculations are halted
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once the liquid abundance drops below 10 wt. %. This results in dramatic improvements in
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speed, and it allows the user to select a wide range of temperatures consistent with the range
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of liquidus and solidus temperatures observed for the pressure interval of interest. At the end of
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the calculations, the user is presented with a new workbook that includes all the data, and a
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diagram displaying the temperatures at which each phase saturates – a phase-in curve – is also
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generated; we note that phase-out curves, which would be present if a phase were to become
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unstable and completely disappear, are not currently displayed.
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As an illustrative example, we use again the same early-erupted Bishop Tuff composition, and
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we calculate a phase diagram for the temperature range of 810-730 ºC, with 1 ºC steps, and
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the pressure range 250-100 MPa, with 25 MPa steps. Of the 567 points in this grid, only 87
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calculations fall at temperatures between the wet liquidus and the 10 wt. % liquid threshold, so
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only a relatively small subset of the grid points actually require calculations to be performed. In
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the resulting phase diagram (Figure 4), the liquid-in curve represents the lowest superliquidus
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temperature on the grid for each pressure. This is also true for the water-in curve in this case,
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because we added enough water to the system for it to be water-saturated at the liquidus for
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all pressures. It can be seen from this example calculation the nearly invariant nature of the
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early-erupted Bishop Tuff compositions, which crystallize over a very narrow temperature
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interval [Gualda and Ghiorso, 2013; Gualda et al., 2012a; Gualda et al., 2012b].
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3.4. A calculation using the rhyolite-MELTS geobarometer
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The new interface also makes it possible to apply the rhyolite-MELTS geobarometer [Gualda
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and Ghiorso, 2014], which uses rhyolite-MELTS to calculate the pressure at which a given melt
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composition can be in simultaneous equilibrium with the expected felsic assemblage (quartz and
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feldspars).
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Parameters for the pressure calculations are set in the same way as for the phase diagram
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calculations and, in fact, the calculations are performed in the same way; the only difference is
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that an extra sheet is included in the output workbook where the pressure calculations are
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made. For proper functioning of the capabilities of this sheet, the user needs to check “Trust
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access to the VBA project object model” within the “Macro Settings” of Microsoft Excel “Trust
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Center”).
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The composition used in the examples above is representative of both early-erupted Bishop Tuff
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bulk rocks [Hildreth, 1979] and quartz-hosted glass inclusions [Anderson et al., 2000]. Early-
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erupted magmas are characterized by the presence of quartz, sanidine, and plagioclase
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[Anderson et al., 2000; Gualda and Ghiorso, 2013; Hildreth, 1979]. The pressure calculations
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(Figure 4) show that all three phases are in simultaneous equilibrium at pressures of ~170 MPa
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(Figure 4b). Even if melt inclusions were entrapped prior to saturation in both feldspars, the
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estimated saturation pressure would still be the same (Figure 4c) [for more details, see Gualda
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and Ghiorso, 2014].
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4. Some current limitations
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MELTS_Excel is in active development, and not all the envisioned functionality is implemented.
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As such, there are some current limitations:
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(1) MELTS_Excel currently only works with rhyolite-MELTS, and there is no interface with
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pMELTS (rhyolite-MELTS effectively replace MELTS, given that the calibration for mafic
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systems is identical, and it takes advantage of the much improved calculation algorithms
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included in rhyolite-MELTS [Ghiorso, 2013]);
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(2) Only equilibrium mode calculations are currently implemented; implementation of
fractionation modes is planned for the near future;
(3) Only calculations using pressure and temperature (as opposed to entropy and volume)
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as independent variables (i.e. Gibbs free-energy minimization and related fO2-constrained
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Korzhinskii potential minimization [Ghiorso and Gualda, 2015]) are currently
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implemented, which precludes isenthalpic or isochoric calculations available through the
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existing MELTS GUI; we intend to eventually implement such capabilities;
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(4) No assimilation mode is currently implemented;
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We envision that, for most users, the new interface will replace the existing GUI. However, one
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of the hallmarks of the GUI is its flexibility and the ability to simulate complex evolution
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histories. In many ways, the new Excel interface is currently less flexible, which may cause
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some advanced users to prefer the GUI for specific calculations. In these cases, the ability to
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import and process tbl files to generate equivalent output (under “Tools” tab) may be a useful
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functionality of MELTS_Excel.
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5. Conclusions
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In this paper we present MELTS_Excel, a new interface for rhyolite-MELTS based on Microsoft
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Excel. It utilizes web services to perform calculations on a remote server at OFM Research and
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deliver results to the user in an Excel workbook. It takes advantage of spreadsheet and graphic
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capabilities of Microsoft Excel to simplify both data input and output. Due to differences in
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capability of web services available in the various versions of Excel, MELTS_Excel currently only
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works on versions 2010 and 2013 of Microsoft Excel for Windows.
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The interface is contained within a macro-enabled workbook, which includes editable cells
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where the user can insert the model input information. Results of simple calculations are shown
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immediately within the interface itself.
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It is also possible to combine a sequence of calculations into an evolutionary path. The user can
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input starting and ending temperatures and pressures, temperature and pressure steps, and the
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prevailing oxidation conditions, and the program will perform the calculations showing the
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magma properties at every step; at the conclusion of the calculations, a series of data sheets
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and diagrams are created in a separate workbook, which can be saved independently of the
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interface.
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Additionally, the user can specify a grid of temperatures and pressures and calculate a phase
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diagram showing the conditions at which different phases are present. Pressure estimation
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using the rhyolite-MELTS geobarometer is also possible using the interface.
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The main advantages of this new interface are that it is simple to use and flexible. The interface
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is built on a popular platform and which is widely available. The interface requires no
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installation and it is distributed for free. The main drawback is that operation of the workbook
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requires an internet connection. The interface is actively being developed, so not all features of
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the GUI are currently implemented in MELTS_Excel.
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We expect that the new interface will facilitate the use of rhyolite-MELTS, particularly for the
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novice user, but also for users performing a large number of simulations. We hope that
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MELTS_Excel will also facilitate the use of MELTS for teaching purposes.
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6. Acknowledgements
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MELTS_Excel can be downloaded for free from: http://melts.ofm-research.org. Financial
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support was provided by NSF (EAR-1321806, EAR-1151337, EAR-0948528 to Gualda and EAR-
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0948734, EAR-1321924 to Ghiorso) and by a Vanderbilt University Discovery Grant to Gualda.
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7. References
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Anderson, A. T., A. M. Davis, and F. Q. Lu (2000), Evolution of Bishop Tuff rhyolitic magma
based on melt and magnetite inclusions and zoned phenocrysts, Journal of Petrology, 41(3),
449-473.
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Asimow, P. D., and M. S. Ghiorso (1998), Algorithmic modifications extending MELTS to
calculate subsolidus phase relations, American Mineralogist, 83(9-10), 1127-1132.
343
344
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Ferry, J. M., and E. B. Watson (2007), New thermodynamic models and revised calibrations for
the Ti-in-zircon and Zr-in-rutile thermometers, Contributions to Mineralogy and Petrology,
154(4), 429-437.
346
347
Ghiorso, M. S. (1997), Thermodynamic models of igneous processes, Annual Review of Earth
and Planetary Sciences, 25, 221-241.
348
349
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Ghiorso, M. S. (2013), A globally convergent saturation state algorithm applicable to
thermodynamic systems with a stable or metastable omni-component phase, Geochimica Et
Cosmochimica Acta, 103, 295-300.
351
352
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Ghiorso, M. S., and R. O. Sack (1995), Chemical mass-transfer in magmatic processes. 4. A
revised and internally consistent thermodynamic model for the interpolation and extrapolation
of liquid-solid equilibria in magmatic systems at elevated-temperatures and pressures,
Contributions to Mineralogy and Petrology, 119(2-3), 197-212.
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356
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Ghiorso, M. S., and G. A. R. Gualda (2013), A method for estimating the activity of titania in
magmatic liquids from the compositions of coexisting rhombohedral and cubic iron-titanium
oxides, Contributions To Mineralogy and Petrology, 165(1), 73-81.
358
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Ghiorso, M. S., and G. A. R. Gualda (2015), Chemical thermodynamics and the study of
magmas, in Encyclopedia of Volcanoes, edited by H. Sigurdsson, p. in press.
360
361
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Ghiorso, M. S., M. M. Hirschmann, P. W. Reiners, and V. C. Kress (2002), The pMELTS: A
revision of MELTS for improved calculation of phase relations and major element partitioning
related to partial melting of the mantle to 3 GPa, Geochemistry Geophysics Geosystems, 3.
363
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Gualda, G. A. R., and M. S. Ghiorso (2013), The Bishop Tuff giant magma body: an alternative
to the Standard Model, Contributions to Mineralogy and Petrology, 166(3), 755-775.
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Gualda, G. A. R., and M. S. Ghiorso (2014), Phase-equilibrium geobarometers for silicic rocks
based on rhyolite-MELTS. Part 1: Principles, procedures, and evaluation of the method,
Contributions to Mineralogy and Petrology C7 - 1033, 168(1), 1-17.
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Gualda, G. A. R., M. S. Ghiorso, R. V. Lemons, and T. L. Carley (2012a), Rhyolite-MELTS: A
modified calibration of MELTS optimized for silica-rich, fluid-bearing magmatic systems, Journal
of Petrology, 53(5), 875-890.
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Gualda, G. A. R., A. S. Pamukcu, M. S. Ghiorso, A. T. Anderson, Jr., S. R. Sutton, and M. L.
Rivers (2012b), Timescales of quartz crystallization and the longevity of the Bishop giant
magma body, Plos One, 7(5), e37492.
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Hayden, L. A., E. B. Watson, and D. A. Wark (2008), A thermobarometer for sphene (titanite),
Contributions to Mineralogy and Petrology, 155(4), 529-540.
376
377
Hildreth, W. (1979), The Bishop Tuff: Evidence for the origin of compositional zonation in silicic
magma chambers, Geological Society of America Special Paper, 180, 43-75.
378
379
380
Reid, M. R., J. A. Vazquez, and A. K. Schmitt (2011), Zircon-scale insights into the history of a
Supervolcano, Bishop Tuff, Long Valley, California, with implications for the Ti-in-zircon
geothermometer, Contributions to Mineralogy and Petrology, 161(2), 293-311.
381
382
383
Thomas, J. B., E. B. Watson, F. S. Spear, P. T. Shemella, S. K. Nayak, and A. Lanzirotti (2010),
TitaniQ under pressure: the effect of pressure and temperature on the solubility of Ti in quartz,
Contributions to Mineralogy and Petrology, 160(5), 743-759.
384
385
Wark, D. A., and E. B. Watson (2006), TitaniQ: a titanium-in-quartz geothermometer,
Contributions to Mineralogy and Petrology, 152(6), 743-754.
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387
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8. Figure captions
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Figure 1. Screenshot showing the “Input” sheet of MELTS_Excel, where the system
391
composition is defined, as well as temperature, pressure and oxygen fugacity conditions for
392
simple calculations. Several buttons that trigger sample calculations can be seen. The result of
393
an “Equilibrate” calculation at the conditions listed are displayed on the right portion, including
394
the names, abundances and compositions of phases present, as well as the affinities of all
395
phases that are not present but which are included in the calculation. More detailed results are
396
presented in the “Results” sheet.
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Figure 2. Graphics displaying some of the results of an isobaric sequence of calculations. The
398
composition is the same as shown in Figure 1. The temperature range is 765-755 ºC, in 0.5 ºC
399
steps, at 175 MPa, with fO2 constrained along the Ni-NiO buffer. Top: Variation in mass as a
400
function of temperature for all phases present, for all solids, and for the whole system. Middle:
401
Variation in liquid composition as a function of temperature; note that SiO2 is shown on a
402
different vertical scale (to the right) than the other oxides. Bottom: Variation in the composition
403
of feldspars as a function of temperature; the highest temperature feldspar appears at 760 ºC,
404
while a lower temperature feldspar saturates at 759.9 ºC; the zigzag lines demonstrate the
405
coexistence of two feldspars within that temperature range.
406
Figure 3. Example of the use of rhyolite-MELTS to calculate aTiO2 and Ti-in-zircon as a function
407
of temperature using the variation in the affinity of rutile as a function of temperature. Top:
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Variation in aTiO2 as a function of temperature calculated using the relationship shown on the
409
right panel [see Ghiorso and Gualda, 2013]. Bottom: Variation in Ti-in-zircon as a function of
410
temperature calculated using the Ti-in-zircon calibration of Ferry & Watson [2007]; panel on the
411
right shows histogram of Ti abundances in zircon from early-erupted Bishop Tuff [Reid et al.,
412
2011], on the same vertical scale as the plot on the left; the histogram shows that the vast
413
majority of zircons are expected to have crystallized at temperatures below 758 ºC, consistent
414
with the range of temperatures over which crystallization of early-erupted magmas should have
415
taken place (see Figure 2).
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Figure 4. Example calculation of a phase diagram and application of the rhyolite-MELTS
417
geobarometer. Top: Phase diagram calculated for the same composition as in the prior
418
examples, over a temperature range of 810-730 ºC (1 ºC steps) and a pressure range of 250-
419
100 MPa (25 MPa steps). Bottom: Diagrams showing the application of the rhyolite-MELTS
15
420
geobarometer; left panel shows calculation of the pressure at which quartz and two feldspars
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are expected to be in equilibrium with the input glass composition; right panel shows calculation
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of the pressure at which quartz and one feldspar are expected to be in equilibrium with the
423
input glass compositions [for further details, see Gualda and Ghiorso, 2014].
16
120 100 liquid water Mass (g) 80 solids orthopyroxene 60 spinel 40 quartz feldspar1 20 feldspar2 0 765 764 763 762 761 760 759 758 757 756 total 755 Temperature (ºC) Temperature (ºC) 763 761 759 757 14 wt. % (others) 12 10 Fe2O3 (wt%) 74 Cr2O3 (wt%) 8 73.8 6 73.7 73.6 4 761 759 757 FeO (wt%) MnO (wt%) MgO (wt%) 73.5 NiO (wt%) 73.4 CoO (wt%) 73.3 755 CaO (wt%) 2 763 Al2O3 (wt%) 74.1 73.9 0 765 TiO2 (wt%) 755 74.2 wt. % (SiO2) 765 Na2O (wt%) Temperature (ºC) 0.9 0.8 Mole frac=on 0.7 0.6 0.5 albite 0.4 anorthite 0.3 sanidine 0.2 0.1 0 765 764 763 762 761 760 759 Temperature (ºC) 758 757 756 755 1.0 Chemical affinity for ruOle saturaOon 0.9 0.8 aTiO2 0.7 " A %
liquid−rutile
aTiO2
= exp $ − rutile '
# RT &
0.6 0.5 0.4 AcOvity of TiO2 referenced to ruOle saturaOon 0.3 0.2 0.1 See: Ghiorso & Gualda (2013) 0.0 765 764 763 762 761 760 759 758 757 756 755 Temperature (ºC) 6.0 Ti in zircon (ppm) 5.0 4.0 3.0 2.0 log(Tizircon ) = 5.711−
1.0 4800
− log(aSiO2 ) + log(aTiO2 )
T[K ]
See: Ferry & Watson (2007) Data from Reid et al. (2011) 0.0 765 764 763 762 761 760 759 Temperature (ºC) 758 757 756 755 0 10 20 30 240 Pressure (MPa) 220 liquid orthopyroxene 200 rhm-­‐oxide 180 bioOte spinel 160 feldspar1 140 feldspar2 quartz 120 water 100 730 740 750 760 770 780 790 800 810 Temperature (ºC) Quartz+2 Feldspars Quartz+1 Feldspar 810 810 800 800 790 790 quartz 780 780 770 feldspar1 770 760 feldspar2 760 750 quartz feldspar1 750 740 740 0 100 200 300 0 30 100 200 300 20 delta_q2f 20 10 fit_q2f 169 P_q2f 0 0 100 200 300 15 delta_q1f 10 fit_q1f 170 5 P_q1f 0 0 100 200 300